UGC NET CSE | December 2008 | Part 2 | Question: 12

Question

A relation R in {1,2,3,4,5,6} is given by {(1,2),(2,3),(3,4),(4,4),(4,5)}. This relation is:

• A. reflexive     
• B. symmetric
• C. transitive    
• D. not reflexive, not symmetric and not transitive

Comments

D.....

Answer 1

"Relation R in {1,2,3,4,5,6} is given by {(1,2),(2,3),(3,4),(4,4),(4,5)}"

Reflexive : The relation R is not reflexive since {(1,1)(2,2)(3,3)(4,4)(5,5)} is not present in relation.
Symmetric : This relation is not symmetric since (1,2) is present but it didnot contain (2,1), similarly we can check for other elements.
Transitive :  This relation is not transitive, since (1,2) and (2,3) is present the relation doesnot contains (1,3), similarly we can check for other elements.

So this relation is not reflexive, not symmetric, not transitive.
Option D is correct.